The A77ii would be great if you want to replicate your experience shooting the 7D, but with the addition of EVF, greater dynamic range, more MP and in-body stabilization. There are zoom and macro lenses that will suit your needs very well, especially if you are willing to try Tamron glass. Sony and Minolta glass is good as well.
I enjoy shooting sports--and shooting in general--with the a77ii, especially at the price I got it and my two a-mount pieces of glass for.
While I have not shot its successors, the a6000 typically gives me better images than my a77ii does SOOC. For sports and wildlife, though, you are going to pay somewhat of a premium for proper e-mount zoom glass. If you are willing to do so, though, IMO you will be happier with your conversion. Just a few things:
--there is no e-mount glass that goes past 300mm.
--once you put an adapter on the a6x00 body it becomes somewhat awkward to shoot with.
--you will have to buy the new a6500 if you want IBIS.
If you are prepared to spend more money, and don't mind being limited to 300mm, go for the a6500. The weight savings and performance will knock your socks off. If you want to spend considerably less money and don't mind a bigger body, grab a deal on an a77ii--they're out there.
Sony A99ii, RX-100ii, Sonnar T* 135mm f/1.8 ZA, Minolta HS 200 2.8 APO, Zeiss 24/2 ZA, Minolta 2xTC APO, HVL-F43M